# References for Electrostatics Calculations Used in Molecular Dynamics

I'm looking for classic references that describe the usual electrostatic contributions which have to be calculated in molecular dynamics simulations. I find it very hard to apprehend what different interaction potentials actually do to calculate electrostatic interactions.

Here are some questions that confuse me:

• Is the description of electrostatics in non-periodic simulations a strict subset of the calculations performed in periodic simulations? That is, there are these techniques like Ewald summation which speed up calculations by leveraging the periodic nature of the system and splitting the interactions into short- and long-range parts which can be described in different ways that manages to avoid the $$O(N^2)$$ nature of the problem. Does this type of description completely replace the simpler $$O(N^2)$$ approach one might take in a non-periodic simulation?
• Why do electrostatics for most potentials seem to stop at charge and dipole interactions? Shouldn't we really consider interactions involving higher-order mutipoles as well?

As you can see, I have a lot of basic holes in my knowledge of the way these calculations are carried out even though I have personally implemented some of these methods before. If someone could provide me with references that discuss the different types of approximations (and how they relate to one another) to the electrostatic part of the interactions needed for MD simulations, that would be greatly appreciated.

• As for your second question, this is because (1) the interactions between higher-order multipoles are rather short-ranged, (2) calculating these interactions are relatively costly and more difficult to code, and (3) high-order multipoles are harder to parameterize. If you are doing ab initio calculations instead of molecular mechanics, you will see that much higher order multipoles are used (when the Coulomb interaction is calculated by multipolar expansion). For example DMol3 uses up to octupoles and hexadecapoles, and BDF uses up to 256-poles. Jul 1 at 7:44